Question

The radius of a circle is $25$cm. Two chords of lengths $14$cm and $48$cm are parallel to each other. Find the distance between them.

Answer 1

$AB=14$

$AP+PB=14$

$[\because AP=PB]$

$2AP=14$

$AP=7$

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$CQ=24$

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Consider $\Delta$ABO

$A{O}^2=P{O}^2+P{A}^2$ $[\because AB=14,PA=PB=7]$

${25}^2=P{O}^2+7^2$

$\Rightarrow P{O}^2=625-49$

$\Rightarrow P{O}^2=576$

$\Rightarrow PO=24$

Consider $\Delta$COD

$C{O}^2=O{Q}^2+C{Q}^2$

$2S^2=O{Q}^2+{24}^2$

$\Rightarrow O{Q}^2={25}^2-{24}^2$

$\Rightarrow O{A}^2=49$

$\Rightarrow OQ=7$

$\therefore$ Distance between the chords $QP=PO-OQ$

$=24-7$

$=17$cm.